The father of aerobics, Dr. Kenneth Copper, touched upon that subject in the first edition of "Aerobics". From what I remember, it doesn't make a difference to at least conditioning when you eat, or what time you run. First thing in the moring is perfectly ok. However, he did note that it better to not run within 2 hours of eating. The blood is at the stomach at this time.
However, in my experience first of the morning runs are very nice but I find that if I do more than two days in a row I much more sore than if I run in the late morning and later.